Some aspects of a coupled system of nonlinear integral equations

In the present work we take a system of two integral equations and prove the existence and uniqueness of their solution. We investigate four aspects of the problem, namely, error estimation and rate of convergence of the iteration leading to the solution, Ulam-Hyers stability, well-posedness and data dependence of the solution sets. We give some new de nitions pertaining to the system we analyze here. In order to establish our results we utilize the coupled contraction mapping principle due to Bhaskar and Lakshmikantham (Nonlinear Anal. TMA 65(2006), 1379-1393) and several related results which we deduce here.